// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PARAMETRIZEDLINE_H
#define EIGEN_PARAMETRIZEDLINE_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 * \class ParametrizedLine
 *
 * \brief A parametrized line
 *
 * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
 * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
 * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
 *
 * \tparam _Scalar the scalar type, i.e., the type of the coefficients
 * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
 */
template<typename _Scalar, int _AmbientDim, int _Options>
class ParametrizedLine
{
  public:
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar, _AmbientDim)
	enum
	{
		AmbientDimAtCompileTime = _AmbientDim,
		Options = _Options
	};
	typedef _Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
	typedef Matrix<Scalar, AmbientDimAtCompileTime, 1, Options> VectorType;

	/** Default constructor without initialization */
	EIGEN_DEVICE_FUNC inline ParametrizedLine() {}

	template<int OtherOptions>
	EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
		: m_origin(other.origin())
		, m_direction(other.direction())
	{
	}

	/** Constructs a dynamic-size line with \a _dim the dimension
	 * of the ambient space */
	EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim)
		: m_origin(_dim)
		, m_direction(_dim)
	{
	}

	/** Initializes a parametrized line of direction \a direction and origin \a origin.
	 * \warning the vector direction is assumed to be normalized.
	 */
	EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)
		: m_origin(origin)
		, m_direction(direction)
	{
	}

	template<int OtherOptions>
	EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);

	/** Constructs a parametrized line going from \a p0 to \a p1. */
	EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
	{
		return ParametrizedLine(p0, (p1 - p0).normalized());
	}

	EIGEN_DEVICE_FUNC ~ParametrizedLine() {}

	/** \returns the dimension in which the line holds */
	EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }

	EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
	EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }

	EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
	EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }

	/** \returns the squared distance of a point \a p to its projection onto the line \c *this.
	 * \sa distance()
	 */
	EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const
	{
		VectorType diff = p - origin();
		return (diff - direction().dot(diff) * direction()).squaredNorm();
	}
	/** \returns the distance of a point \a p to its projection onto the line \c *this.
	 * \sa squaredDistance()
	 */
	EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const
	{
		EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p));
	}

	/** \returns the projection of a point \a p onto the line \c *this. */
	EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const
	{
		return origin() + direction().dot(p - origin()) * direction();
	}

	EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;

	template<int OtherOptions>
	EIGEN_DEVICE_FUNC Scalar
	intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;

	template<int OtherOptions>
	EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;

	template<int OtherOptions>
	EIGEN_DEVICE_FUNC VectorType
	intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;

	/** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
	 *
	 * \param mat the Dim x Dim transformation matrix
	 * \param traits specifies whether the matrix \a mat represents an #Isometry
	 *               or a more generic #Affine transformation. The default is #Affine.
	 */
	template<typename XprType>
	EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat,
														 TransformTraits traits = Affine)
	{
		if (traits == Affine)
			direction() = (mat * direction()).normalized();
		else if (traits == Isometry)
			direction() = mat * direction();
		else {
			eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
		}
		origin() = mat * origin();
		return *this;
	}

	/** Applies the transformation \a t to \c *this and returns a reference to \c *this.
	 *
	 * \param t the transformation of dimension Dim
	 * \param traits specifies whether the transformation \a t represents an #Isometry
	 *               or a more generic #Affine transformation. The default is #Affine.
	 *               Other kind of transformations are not supported.
	 */
	template<int TrOptions>
	EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(
		const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t,
		TransformTraits traits = Affine)
	{
		transform(t.linear(), traits);
		origin() += t.translation();
		return *this;
	}

	/** \returns \c *this with scalar type casted to \a NewScalarType
	 *
	 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
	 * then this function smartly returns a const reference to \c *this.
	 */
	template<typename NewScalarType>
	EIGEN_DEVICE_FUNC inline
		typename internal::cast_return_type<ParametrizedLine,
											ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options>>::type
		cast() const
	{
		return typename internal::
			cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options>>::type(
				*this);
	}

	/** Copy constructor with scalar type conversion */
	template<typename OtherScalarType, int OtherOptions>
	EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(
		const ParametrizedLine<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other)
	{
		m_origin = other.origin().template cast<Scalar>();
		m_direction = other.direction().template cast<Scalar>();
	}

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	 * determined by \a prec.
	 *
	 * \sa MatrixBase::isApprox() */
	EIGEN_DEVICE_FUNC bool isApprox(
		const ParametrizedLine& other,
		const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
	{
		return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec);
	}

  protected:
	VectorType m_origin, m_direction;
};

/** Constructs a parametrized line from a 2D hyperplane
 *
 * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
 */
template<typename _Scalar, int _AmbientDim, int _Options>
template<int OtherOptions>
EIGEN_DEVICE_FUNC inline ParametrizedLine<_Scalar, _AmbientDim, _Options>::ParametrizedLine(
	const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane)
{
	EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
	direction() = hyperplane.normal().unitOrthogonal();
	origin() = -hyperplane.normal() * hyperplane.offset();
}

/** \returns the point at \a t along this line
 */
template<typename _Scalar, int _AmbientDim, int _Options>
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim, _Options>::VectorType
ParametrizedLine<_Scalar, _AmbientDim, _Options>::pointAt(const _Scalar& t) const
{
	return origin() + (direction() * t);
}

/** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
 */
template<typename _Scalar, int _AmbientDim, int _Options>
template<int OtherOptions>
EIGEN_DEVICE_FUNC inline _Scalar
ParametrizedLine<_Scalar, _AmbientDim, _Options>::intersectionParameter(
	const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
{
	return -(hyperplane.offset() + hyperplane.normal().dot(origin())) / hyperplane.normal().dot(direction());
}

/** \deprecated use intersectionParameter()
 * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
 */
template<typename _Scalar, int _AmbientDim, int _Options>
template<int OtherOptions>
EIGEN_DEVICE_FUNC inline _Scalar
ParametrizedLine<_Scalar, _AmbientDim, _Options>::intersection(
	const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
{
	return intersectionParameter(hyperplane);
}

/** \returns the point of the intersection between \c *this and the given hyperplane
 */
template<typename _Scalar, int _AmbientDim, int _Options>
template<int OtherOptions>
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim, _Options>::VectorType
ParametrizedLine<_Scalar, _AmbientDim, _Options>::intersectionPoint(
	const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
{
	return pointAt(intersectionParameter(hyperplane));
}

} // end namespace Eigen

#endif // EIGEN_PARAMETRIZEDLINE_H
